# Unit Rate

A **unit rate** is how much of something there is per one unit of something else. Examples of unit rate include miles per hour, dollars per pound, cookies per person, and kilometers per liter.

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## Introduction

At the store, Sally sees that 15 pounds of peaches cost $51. She is frustrated because all she really wants to know is the cost of one pound so that she can figure out how many pounds she wants to buy.

$51 per 15 pounds is a rate, a ratio that compares two quantities of different units (in this case, dollars and pounds.) While it's nice to know the cost of 15 pounds of peaches, most shoppers would be more interested in knowing the **unit rate,** or the cost for one pound of peaches. Knowing the cost of one unit makes it easier to compare prices and to find the cost of multiple units.

## Which quantity listed below is a unit rate?

A. $25,000 per 6 months

B. 5 giraffes per 3 cages

C. 2000 lizards per year

Only C is a unit rate because the 2000 lizards are expressed as a quantity per

1year. Neither A nor B are unit rates because A is expressed a quantity per 6 months and B is expressed as quantity per 3 cages.

Equivalent ratios always have the same unit rate. For example, Store A that charges $144 for 12 pizzas has the same unit rate per pizza as Store B that charges $48 for 4 pizzas. Both stores charge $12 per pizza.

## Is the unit rate for 20 bananas per 6 monkeys equivalent to the unit rate for 15 bananas per 4 monkeys?

No, the unit rates of bananas per monkey are not equivalent. 20 bananas per 6 monkeys is equivalent to 10 bananas per 3 monkeys. \(\frac{10}{3} \neq \frac{15}{4}\) so the unit rates are not equivalent.

## Finding a Unit Rate

We can convert any rate into a unit rate by dividing the first quantity by the second so that we know the amount of the first quantity per one unit of the second.

For example, if a school outing has 126 kids on 3 buses, then the unit rate of kids per bus is \(126 \div 3 = 42.\)

## What is the unit rate in kilometers per hour of a plane that travels 2700 kilometers in 3 hours?

The unit rate is \(2700 \div 3 = 900\) kilometers per hour.

## If you have \(a\) items for \(b\) dollars, then what is the unit cost in dollars per item?

We want to find dollars per item so we want to divide \(b\) by \(a.\) The unit rate is \(\frac{b}{a}\) dollars per one item.